Abstract
In this paper, we explore the open string amplitude’s dual role as a space-time S-matrix and a 2D holomorphic CFT correlation function. We pursue this correspondence in two directions. First, beginning with a general disk integrand dressed with a Koba-Nielsen factor, we demonstrate that exchange symmetry for the factorization residue of the amplitude forces the integrand to be expandable on SL(2,R) conformal blocks. Furthermore, positivity constraints associated with unitarity imply the SL(2,R) blocks must come in linear combinations for which the Virasoro block emerges at the “kink” in the space of solutions. In other words, Virasoro symmetry arises at the boundary of consistent factorization. Next, we consider the low energy EFT description, where unitarity manifests as the EFThedron in which the couplings must live. The existence of a worldsheet description implies, through the Koba-Nielsen factor, monodromy relations which impose algebraic identities amongst the EFT couplings. We demonstrate at finite derivative order that the intersection of the “monodromy plane” and the four-dimensional EFThedron carves out a tiny island for the couplings, which continues to shrink as the derivative order is increased. At the eighth derivative order, on a three-dimensional monodromy plane, the intersection fixes the width of this island to around 1.5% (of ζ(3)) and 0.2% (of ζ(5)) with respect to the toroidally compactified Type-I super string answer. This leads us to conjecture that the four-point open superstring amplitude can be completely determined by the geometry of the intersection of the monodromy plane and the EFThedron.
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References
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
D. Simmons-Duffin, The Conformal Bootstrap, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, (2016) [DOI] [arXiv:1602.07982] [INSPIRE].
D. Poland and D. Simmons-Duffin, The conformal bootstrap, Nature Phys. 12 (2016) 535 [INSPIRE].
D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, Rev. Mod. Phys. 91 (2019) 015002 [arXiv:1805.04405] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap II: two dimensional amplitudes, JHEP 11 (2017) 143 [arXiv:1607.06110] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part III: higher dimensional amplitudes, JHEP 12 (2019) 040 [arXiv:1708.06765] [INSPIRE].
A. Homrich, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix Bootstrap IV: Multiple Amplitudes, JHEP 11 (2019) 076 [arXiv:1905.06905] [INSPIRE].
S.D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices, JHEP 02 (2020) 114 [arXiv:1910.14392] [INSPIRE].
A. Bose, P. Haldar, A. Sinha, P. Sinha and S.S. Tiwari, Relative entropy in scattering and the S-matrix bootstrap, SciPost Phys. 9 (2020) 081 [arXiv:2006.12213] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:1412.3479] [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation, Nucl. Phys. B 873 (2013) 419 [arXiv:1106.2645] [INSPIRE].
J.J.M. Carrasco, C.R. Mafra and O. Schlotterer, Abelian Z-theory: NLSM amplitudes and α’-corrections from the open string, JHEP 06 (2017) 093 [arXiv:1608.02569] [INSPIRE].
C.R. Mafra and O. Schlotterer, Non-abelian Z -theory: Berends-Giele recursion for the α′-expansion of disk integrals, JHEP 01 (2017) 031 [arXiv:1609.07078] [INSPIRE].
Y.-t. Huang, O. Schlotterer and C. Wen, Universality in string interactions, JHEP 09 (2016) 155 [arXiv:1602.01674] [INSPIRE].
T. Azevedo, M. Chiodaroli, H. Johansson and O. Schlotterer, Heterotic and bosonic string amplitudes via field theory, JHEP 10 (2018) 012 [arXiv:1803.05452] [INSPIRE].
N. Arkani-Hamed, S. He and T. Lam, Stringy canonical forms, JHEP 02 (2021) 069 [arXiv:1912.08707] [INSPIRE].
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
B. Bellazzini, C. Cheung and G.N. Remmen, Quantum Gravity Constraints from Unitarity and Analyticity, Phys. Rev. D 93 (2016) 064076 [arXiv:1509.00851] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories, Phys. Rev. D 96 (2017) 081702 [arXiv:1702.06134] [INSPIRE].
C. de Rham, S. Melville and A.J. Tolley, Improved Positivity Bounds and Massive Gravity, JHEP 04 (2018) 083 [arXiv:1710.09611] [INSPIRE].
W.-M. Chen, Y.-T. Huang, T. Noumi and C. Wen, Unitarity bounds on charged/neutral state mass ratios, Phys. Rev. D 100 (2019) 025016 [arXiv:1901.11480] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-Hedron, arXiv:2012.15849 [INSPIRE].
M.B. Green and C. Wen, Superstring amplitudes, unitarily, and Hankel determinants of multiple zeta values, JHEP 11 (2019) 079 [arXiv:1908.08426] [INSPIRE].
E. Plahte, Symmetry properties of dual tree-graph n-point amplitudes, Nuovo Cim. A 66 (1970) 713 [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
S. Stieberger, Open & Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].
R.H. Boels and T. Hansen, String theory in target space, JHEP 06 (2014) 054 [arXiv:1402.6356] [INSPIRE].
D.D. Coon, Uniqueness of the veneziano representation, Phys. Lett. B 29 (1969) 669 [INSPIRE].
S. Matsuda, Uniqueness of the veneziano representation, Phys. Rev. 185 (1969) 1811 [INSPIRE].
N.N. Khuri, Derivation of a veneziano series from the Regge representation, Phys. Rev. 185 (1969) 1876 [INSPIRE].
E. Weimar, Alternatives to the Veneziano Amplitude, DESY-74-3 [INSPIRE].
P.G.O. Freund, finite energy sum rules and bootstraps, Phys. Rev. Lett. 20 (1968) 235 [INSPIRE].
M. Froissart, Asymptotic behavior and subtractions in the Mandelstam representation, Phys. Rev. 123 (1961) 1053 [INSPIRE].
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
D.J. Gross and J.L. Manes, The High-energy Behavior of Open String Scattering, Nucl. Phys. B 326 (1989) 73 [INSPIRE].
S. Caron-Huot, Z. Komargodski, A. Sever and A. Zhiboedov, Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude, JHEP 10 (2017) 026 [arXiv:1607.04253] [INSPIRE].
E. Perlmutter, Virasoro conformal blocks in closed form, JHEP 08 (2015) 088 [arXiv:1502.07742] [INSPIRE].
M. Bianchi, D. Consoli and P. Di Vecchia, On the N-pion extension of the Lovelace-Shapiro model, JHEP 03 (2021) 119 [arXiv:2002.05419] [INSPIRE].
R. Kleiss and H. Kuijf, Multi-Gluon Cross-sections and Five Jet Production at Hadron Colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
T. Terasoma, Selberg Integrals and Multiple Zeta Values, Compos. Math. 133 (2002) 1 [math/9908045].
S. Stieberger, Constraints on Tree-Level Higher Order Gravitational Couplings in Superstring Theory, Phys. Rev. Lett. 106 (2011) 111601 [arXiv:0910.0180] [INSPIRE].
O. Schlotterer and S. Stieberger, Motivic Multiple Zeta Values and Superstring Amplitudes, J. Phys. A 46 (2013) 475401 [arXiv:1205.1516] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
D. Mazac and M.F. Paulos, The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices, JHEP 02 (2019) 162 [arXiv:1803.10233] [INSPIRE].
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive Moments for Scattering Amplitudes, arXiv:2011.00037 [INSPIRE].
J.J.M. Carrasco, L. Rodina, Z. Yin and S. Zekioglu, Simple encoding of higher derivative gauge and gravity counterterms, Phys. Rev. Lett. 125 (2020) 251602 [arXiv:1910.12850] [INSPIRE].
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Huang, Yt., Liu, JY., Rodina, L. et al. Carving out the space of open-string S-matrix. J. High Energ. Phys. 2021, 195 (2021). https://doi.org/10.1007/JHEP04(2021)195
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DOI: https://doi.org/10.1007/JHEP04(2021)195